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A Furstenberg–Zimmer structure theorem for \(\varvec{\sigma }\)-finitemeasure spaces

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Abstract

We show that an analog of the Furstenberg–Zimmer structure theorem holds for \(\sigma \)-finite non atomic measure spaces and measure preserving strongly recurrent actions of discrete groups. We adapt the idea of Tao in associating Hilbert modules to measure preserving extensions and show that for an isomorphic copy of the \(L^2\)-space, the tools of Zimmer structure theory could be applied.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, 14115-134, Iran

    MASSOUD AMINI & JUMAH SWID

Authors
  1. MASSOUD AMINI
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  2. JUMAH SWID
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Correspondence to MASSOUD AMINI.

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Communicated by Anish Ghosh.

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AMINI, M., SWID, J. A Furstenberg–Zimmer structure theorem for \(\varvec{\sigma }\)-finitemeasure spaces. Proc Math Sci 132, 16 (2022). https://doi.org/10.1007/s12044-022-00661-y

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  • DOI: https://doi.org/10.1007/s12044-022-00661-y

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